Review Problems STT 231
1. Which function defines a probability space on S = {a1, a2, a3}?
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(i) P(a1) = ,
P(a2) = ,
P(a3) = .
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1
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(ii) P(a1) = ,
P(a2) =
, P(a3) = .
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(iii) P(a1) = , P(a2) = ,
P(a3) = .
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(iv) P(a1) = 0,
P(a2) = ,
P(a3) = .
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2. A class contains 5 freshmen, 4 sophomores, 8 juniors and 3 seniors. A student is chosen at
random to represent the class. Find the probability that the student is (i) a sophomore, (ii) a
senior, (iii) a junior or senior.
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, P(B) = , and P(A  B) = .
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 means OR.
3. Let A and B be events with P(A) =
 means AND;
Find
(i) P(A  B),
(ii) P(Ac), P(Bc)
(iii) P(Ac  Bc)
(iv) P(Ac  Bc),
(v) P(A  Bc), (vi) P(B  Ac).
4. Let A and B be events with P(A) = 3/8, P(B) = 5/8 and P(A  B) = ¾.
Find P(A B) and P(B A).
5. Suppose a test for TB has the following properties: if the person tested has TB, 99% of time
the test will return a positive result; if a person tested does not have TB, 95% of the time the test
will return a negative result. Among the test group, 4% actually have TB.
(i) What proportion of the tests will return a positive result?
(ii) What proportion of those tested positive actually have TB?
The next three questions are based on a regression equation for 55 college students
with x left forearm length (cm) and y height (cm). The forearm lengths ranged
from 22 cm to 31 cm. The regression equation is y = 30.3 + 1.49x.
6. One student's left forearm length was 27 cm, and his height was 75 inches. What is
the estimated height for this student, based on the regression equation?
What is the residual?
7. One student's left forearm length was 22 cm. and her height was 63 inches. What
is the estimated height for this student, based on the regression equation? What is the
residual?
8. The instructor's left forearm length is 35 cm. Is there any problem with using the
regression equation to estimate the instructor's height?"
9. You wish to describe the relationship between exam grades and the amount of time
students watch the Discovery Channel. The correlation turns out to be r +0.30. What does
this mean?
A) The more a student watches the Discovery Channel, the higher his or
her exam grades tend to be.
B) The more a student watches the Discovery Channel, the lower his or
her exam grades tend to be.
C) In order to increase your exam grades, it is recommended that you
spend more time watching the Discovery ChanneL
D) 30% of the variation in exam grades is explained by the linear
relationship with time spent watching the Discovery Channel.
10. A group of adults aged 20 to 80 were tested to see how far away they could
first hear an ambulance coming towards them. An equation describing the linear
relationship between distance (in feet) and age was found to be:
Distance = 600 – 3 Age
Based on the equation, what is the strength of the relationship between distance and age?
A) There is a strong relationship.
B) There is a weak relationship.
C) There is no relationship.
D) Strength cannot be determined from the equation.
11. Which of the following is a possible value of r 2 and indicates the
strongest linear relationship between two quantitative variables?
A) -90%
B) 0%
C) 85%
D) 120%
12. Suppose that a simple linear regression analysis results in r2 = 0 .36 and fitted regression
line y = 7 -3x. What is the value of the correlation coefficient r?
A) 0.6
(B) 0 .8
(C) -0.36
(D) -0.8
(E) -0.6
A linear regression analysis obtains the following results:
CEO Compensation= .0005Sales + $50,000; r = .20
13. Which one of the following is true?
(A) Increasing sales by $100,000 increases the predicted CEO compensation by $50,000.
(B) Increasing sales by $100,000 increases the predicted CEO compensation by $5,000
(C) Increasing sales by $1 increases the predicted CEO compensation by $100,000
(D) A company with no sales has a predicted CEO compensation of $50,000
(E) A company with $500,000,000 in sales has a predicted CEO compensation of
$600,000
14. What percentage of the variation in CEO Compensation is "explained" by
the fitted regression line?
(A) 0%
(B) 4%
(C) -4%
(D) 16%
(E) 20%
15. One
of the points used in the regression analysis is a company with Sales =
$500,000,000 and CEO Compensation= $700,000. This point has a residual of
(A) -$100,000
(B) $50,000
(C) $0
(D) -$50,000
(E) None of these
Answer Key:
1. ANS: (i) No
2. ANS: (i)
(ii) No
(iii) Yes
(iv) Yes
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; (ii)
; (iii)
.
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20
20
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;
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2 2
4. ,
5 3
3. (i)
5. (i) 0.0876
(ii)
5 1
, ;
8 2
(iii)
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;
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(iv)
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(v)
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;
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(vi)
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(ii) 0.452
6. The estimated height is 70.53 inches. The residual is 4.47 inches.
7. The estimated height is 63.08 inches. The residual is -0.08 inches.
8. The instructor's left forearm length is larger than any of the students, so using the
regression equation would be an extrapolation.
9. A
12. E
10. D
13. D
11. C
14. B
15. E